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Showing posts from May, 2009

Frequently misunderstood logic: modus tollens

Back when I was in upper school I studied Further Mathematics and one of the topics I loved was logic. We learnt about syllogism and modus ponens , and my favorite modus tollens . Modus tollens is fun because it is often applied incorrectly in informal arguments to come to the wrong conclusion. Here's an example. The other day I saw a tweet which read: "A fear of weapons is a sign of retarded sexual and emotional maturity." - Sigmund Freud, General Introduction to Psychoanalysis (1952) Simplifying that a little (and assuming we agree with Freud) it can be written "If a person is fearful of weapons, then that person is sexually and emotionally immature". If we write "fearful of weapons" as F and "sexually and emotionally immature" as I , this statement can be rewritten F => I (the => is read as implies and make the entire statement read as F implies I or If F , then I ). So if we come across someone who satisfies F (i.e. t